Question

Find the missing number: \(2, 6, 12, 20, 30, ?\)

• A. \(38\)
• B. \(40\)
• C. \(42\)
• D. \(44\)

Hint:

In number series questions, checking the first differences often reveals a simple pattern such as constant increase, arithmetic progression, or multiplication.

Answer 1

The Correct Option is C

Step 1: Understanding the Question:
This is a number series completion problem where we need to identify the underlying mathematical pattern governing the sequence.
Step 2: Key Formula or Approach:
Examine the differences between consecutive terms to check for an arithmetic progression of the differences.
Step 3: Detailed Explanation:
Let's find the differences between the numbers:
\(6 - 2 = 4\)
\(12 - 6 = 6\)
\(20 - 12 = 8\)
\(30 - 20 = 10\)
The differences are \(4, 6, 8, 10\).
Observe that these differences are consecutive even numbers, increasing by \(2\) each time.
The next difference should be \(10 + 2 = 12\).
Next term = \(30 + 12 = 42\).
Alternatively, the pattern can be seen as \(n^2 + n\):
\(1^2 + 1 = 2\)
\(2^2 + 2 = 6\)
\(3^2 + 3 = 12\)
\(4^2 + 4 = 20\)
\(5^2 + 5 = 30\)
The next term is \(6^2 + 6 = 36 + 6 = 42\).
Step 4: Final Answer:
The missing number is \(42\).